Question

prove that the line segments joining the mid point of two sides of a triangle is parallel to the third side and equal to half of it​

Answer 1

Answer:

The line segment joining the mid-points of two sides of a triangle is parallel to the third side.

You can prove this theorem using the following clue:

Observe the figure in which E and F are mid-points of AB and AC respectively and CD || BA.

∆ AEF ≅ ∆ CDF (ASA Rule)

So, EF = DF and BE = AE = DC. Therefore, BCDE is a parallelogram. This gives EF || BC.

You will see that converse of the above theorem is also true which is stated as below: